A numerical study on indentation properties of cortical bone tissue : Influence of anisotropy

Purpose: The purpose of this study is to investigate the effect of anisotropy of cortical bone tissue on measurement of properties such as direction-dependent moduli and hardness. Methods: An advanced three-dimensional finite element model of microindentation was developed. Different modelling schemes were considered to account for anisotropy of elastic or/and plastic regimes. The elastic anisotropic behaviour was modelled employing an elasticity tensor, and Hill’s criteria were used to represent the direction-dependent post-yield behaviour. The Oliver–Pharr method was used in the data analysis. Results: A decrease in the value of the transverse elasticity modulus resulted in the increased material’s indentation modulus measured in the longitudinal direction and a decreased one in the transverse direction, while they were insensitive to the anisotropy in post-elastic regime. On the other hand, an increase in plastic anisotropy led to a decrease in measured hardness for both directions, but by a larger amount in the transverse one. The size effect phenomenon was found to be also sensitive to anisotropy. Conclusions: The undertaken analysis suggests that the Oliver–Pharr method is a useful tool for first-order approximations in the analysis of mechanical properties of anisotropic materials similar to cortical bone, but not necessarily for the materials with low hardening reserves in the plastic regime.